3. The attempt at a solution
Don't understand why we care about when r1=r0

The tank will overflow when the height of the tank is greater than 1. Why care about r1=r0? What is our motivation for think about the r1=r0 case? That's steady state sure. But they are asking about overflow which I thought just depends on water level

The tank will overflow when the height of the tank is greater than 1. Why care about r1=r0? What is our motivation for think about the r1=r0 case? That's steady state sure. But they are asking about overflow which I thought just depends on water level

Max. outflow rate of tank 1 without spilling is r1(h1max). This obviously must be >= r0.
If r0 > r1(h1max) then tank 1 will spill since more water has to flow out of tank 1 than its hole can accommodate.